Question: Solve for $x$, $ \dfrac{9}{15x + 6} = -\dfrac{10}{20x + 8} - \dfrac{3x - 1}{5x + 2} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15x + 6$ $20x + 8$ and $5x + 2$ The common denominator is $60x + 24$ To get $60x + 24$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{9}{15x + 6} \times \dfrac{4}{4} = \dfrac{36}{60x + 24} $ To get $60x + 24$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{10}{20x + 8} \times \dfrac{3}{3} = -\dfrac{30}{60x + 24} $ To get $60x + 24$ in the denominator of the third term, multiply it by $\frac{12}{12}$ $ -\dfrac{3x - 1}{5x + 2} \times \dfrac{12}{12} = -\dfrac{36x - 12}{60x + 24} $ This give us: $ \dfrac{36}{60x + 24} = -\dfrac{30}{60x + 24} - \dfrac{36x - 12}{60x + 24} $ If we multiply both sides of the equation by $60x + 24$ , we get: $ 36 = -30 - 36x + 12$ $ 36 = -36x - 18$ $ 54 = -36x $ $ x = -\dfrac{3}{2}$